1-3z+275z^2-075z^3=0 eching

$$1-3z+275 { z }^{ 2 } -075 { z }^{ 3 } = 0$$

z uchun yechish

$$z=\frac{3+\sqrt{1091}i}{550}\approx 0,005454545+0,060055071i$$

$$z=\frac{-\sqrt{1091}i+3}{550}\approx 0,005454545-0,060055071i$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 75 ni ko'paytirish.

$$1-3z+275z^{2}-0z^{3}=0$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$1-3z+275z^{2}-0=0$$

Shartlarni qayta saralash.

$$275z^{2}-3z+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 275 ni a, -3 ni b va 1 ni c bilan almashtiring.

$$z=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 275}}{2\times 275}$$

-3 kvadratini chiqarish.

$$z=\frac{-\left(-3\right)±\sqrt{9-4\times 275}}{2\times 275}$$

-4 ni 275 marotabaga ko'paytirish.

$$z=\frac{-\left(-3\right)±\sqrt{9-1100}}{2\times 275}$$

9 ni -1100 ga qo'shish.

$$z=\frac{-\left(-3\right)±\sqrt{-1091}}{2\times 275}$$

-1091 ning kvadrat ildizini chiqarish.

$$z=\frac{-\left(-3\right)±\sqrt{1091}i}{2\times 275}$$

-3 ning teskarisi 3 ga teng.

$$z=\frac{3±\sqrt{1091}i}{2\times 275}$$

2 ni 275 marotabaga ko'paytirish.

$$z=\frac{3±\sqrt{1091}i}{550}$$

z=\frac{3±\sqrt{1091}i}{550} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{1091} ga qo'shish.

$$z=\frac{3+\sqrt{1091}i}{550}$$

z=\frac{3±\sqrt{1091}i}{550} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{1091} ni ayirish.

$$z=\frac{-\sqrt{1091}i+3}{550}$$

Tenglama yechildi.

$$z=\frac{3+\sqrt{1091}i}{550} z=\frac{-\sqrt{1091}i+3}{550}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 75 ni ko'paytirish.

$$1-3z+275z^{2}-0z^{3}=0$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$1-3z+275z^{2}-0=0$$

0 ni ikki tarafga qo’shing.

$$1-3z+275z^{2}=0+0$$

0 olish uchun 0 va 0'ni qo'shing.

$$1-3z+275z^{2}=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-3z+275z^{2}=-1$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$275z^{2}-3z=-1$$

Ikki tarafini 275 ga bo‘ling.

$$\frac{275z^{2}-3z}{275}=-\frac{1}{275}$$

275 ga bo'lish 275 ga ko'paytirishni bekor qiladi.

$$z^{2}-\frac{3}{275}z=-\frac{1}{275}$$

-\frac{3}{275} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{550} olish uchun. Keyin, -\frac{3}{550} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$z^{2}-\frac{3}{275}z+\left(-\frac{3}{550}\right)^{2}=-\frac{1}{275}+\left(-\frac{3}{550}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{550} kvadratini chiqarish.

$$z^{2}-\frac{3}{275}z+\frac{9}{302500}=-\frac{1}{275}+\frac{9}{302500}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{275} ni \frac{9}{302500} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$z^{2}-\frac{3}{275}z+\frac{9}{302500}=-\frac{1091}{302500}$$

z^{2}-\frac{3}{275}z+\frac{9}{302500} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(z-\frac{3}{550}\right)^{2}=-\frac{1091}{302500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(z-\frac{3}{550}\right)^{2}}=\sqrt{-\frac{1091}{302500}}$$

Qisqartirish.

$$z-\frac{3}{550}=\frac{\sqrt{1091}i}{550} z-\frac{3}{550}=-\frac{\sqrt{1091}i}{550}$$

\frac{3}{550} ni tenglamaning ikkala tarafiga qo'shish.

$$z=\frac{3+\sqrt{1091}i}{550} z=\frac{-\sqrt{1091}i+3}{550}$$